Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8041,2,Mod(1,8041)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8041, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8041.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8041 = 11 \cdot 17 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8041.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.2077082653\) |
Analytic rank: | \(1\) |
Dimension: | \(74\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 8041.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.77959 | −1.96547 | −0.982734 | − | 0.185022i | \(-0.940764\pi\) | ||||
−0.982734 | + | 0.185022i | \(0.940764\pi\) | |||||||
\(3\) | −0.489198 | −0.282439 | −0.141219 | − | 0.989978i | \(-0.545102\pi\) | ||||
−0.141219 | + | 0.989978i | \(0.545102\pi\) | |||||||
\(4\) | 5.72614 | 2.86307 | ||||||||
\(5\) | −0.717152 | −0.320720 | −0.160360 | − | 0.987059i | \(-0.551266\pi\) | ||||
−0.160360 | + | 0.987059i | \(0.551266\pi\) | |||||||
\(6\) | 1.35977 | 0.555124 | ||||||||
\(7\) | −1.78399 | −0.674283 | −0.337142 | − | 0.941454i | \(-0.609460\pi\) | ||||
−0.337142 | + | 0.941454i | \(0.609460\pi\) | |||||||
\(8\) | −10.3571 | −3.66180 | ||||||||
\(9\) | −2.76069 | −0.920228 | ||||||||
\(10\) | 1.99339 | 0.630365 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | −2.80122 | −0.808641 | ||||||||
\(13\) | −2.65369 | −0.736000 | −0.368000 | − | 0.929826i | \(-0.619957\pi\) | ||||
−0.368000 | + | 0.929826i | \(0.619957\pi\) | |||||||
\(14\) | 4.95875 | 1.32528 | ||||||||
\(15\) | 0.350829 | 0.0905837 | ||||||||
\(16\) | 17.3364 | 4.33409 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | 7.67358 | 1.80868 | ||||||||
\(19\) | −1.91939 | −0.440339 | −0.220170 | − | 0.975462i | \(-0.570661\pi\) | ||||
−0.220170 | + | 0.975462i | \(0.570661\pi\) | |||||||
\(20\) | −4.10651 | −0.918243 | ||||||||
\(21\) | 0.872723 | 0.190444 | ||||||||
\(22\) | 2.77959 | 0.592611 | ||||||||
\(23\) | 2.92463 | 0.609828 | 0.304914 | − | 0.952380i | \(-0.401372\pi\) | ||||
0.304914 | + | 0.952380i | \(0.401372\pi\) | |||||||
\(24\) | 5.06669 | 1.03423 | ||||||||
\(25\) | −4.48569 | −0.897139 | ||||||||
\(26\) | 7.37616 | 1.44658 | ||||||||
\(27\) | 2.81812 | 0.542347 | ||||||||
\(28\) | −10.2153 | −1.93052 | ||||||||
\(29\) | 3.37416 | 0.626565 | 0.313282 | − | 0.949660i | \(-0.398571\pi\) | ||||
0.313282 | + | 0.949660i | \(0.398571\pi\) | |||||||
\(30\) | −0.975163 | −0.178040 | ||||||||
\(31\) | −2.56007 | −0.459802 | −0.229901 | − | 0.973214i | \(-0.573840\pi\) | ||||
−0.229901 | + | 0.973214i | \(0.573840\pi\) | |||||||
\(32\) | −27.4737 | −4.85672 | ||||||||
\(33\) | 0.489198 | 0.0851585 | ||||||||
\(34\) | 2.77959 | 0.476696 | ||||||||
\(35\) | 1.27939 | 0.216256 | ||||||||
\(36\) | −15.8081 | −2.63468 | ||||||||
\(37\) | 11.2450 | 1.84867 | 0.924334 | − | 0.381583i | \(-0.124621\pi\) | ||||
0.924334 | + | 0.381583i | \(0.124621\pi\) | |||||||
\(38\) | 5.33513 | 0.865473 | ||||||||
\(39\) | 1.29818 | 0.207875 | ||||||||
\(40\) | 7.42764 | 1.17441 | ||||||||
\(41\) | 4.76123 | 0.743579 | 0.371789 | − | 0.928317i | \(-0.378744\pi\) | ||||
0.371789 | + | 0.928317i | \(0.378744\pi\) | |||||||
\(42\) | −2.42581 | −0.374311 | ||||||||
\(43\) | −1.00000 | −0.152499 | ||||||||
\(44\) | −5.72614 | −0.863247 | ||||||||
\(45\) | 1.97983 | 0.295136 | ||||||||
\(46\) | −8.12929 | −1.19860 | ||||||||
\(47\) | −0.457282 | −0.0667014 | −0.0333507 | − | 0.999444i | \(-0.510618\pi\) | ||||
−0.0333507 | + | 0.999444i | \(0.510618\pi\) | |||||||
\(48\) | −8.48091 | −1.22411 | ||||||||
\(49\) | −3.81739 | −0.545342 | ||||||||
\(50\) | 12.4684 | 1.76330 | ||||||||
\(51\) | 0.489198 | 0.0685015 | ||||||||
\(52\) | −15.1954 | −2.10722 | ||||||||
\(53\) | −5.27651 | −0.724784 | −0.362392 | − | 0.932026i | \(-0.618040\pi\) | ||||
−0.362392 | + | 0.932026i | \(0.618040\pi\) | |||||||
\(54\) | −7.83322 | −1.06597 | ||||||||
\(55\) | 0.717152 | 0.0967007 | ||||||||
\(56\) | 18.4770 | 2.46909 | ||||||||
\(57\) | 0.938964 | 0.124369 | ||||||||
\(58\) | −9.37878 | −1.23149 | ||||||||
\(59\) | −1.26303 | −0.164432 | −0.0822162 | − | 0.996615i | \(-0.526200\pi\) | ||||
−0.0822162 | + | 0.996615i | \(0.526200\pi\) | |||||||
\(60\) | 2.00890 | 0.259347 | ||||||||
\(61\) | −13.8801 | −1.77717 | −0.888585 | − | 0.458713i | \(-0.848311\pi\) | ||||
−0.888585 | + | 0.458713i | \(0.848311\pi\) | |||||||
\(62\) | 7.11595 | 0.903726 | ||||||||
\(63\) | 4.92502 | 0.620495 | ||||||||
\(64\) | 41.6931 | 5.21163 | ||||||||
\(65\) | 1.90309 | 0.236050 | ||||||||
\(66\) | −1.35977 | −0.167376 | ||||||||
\(67\) | 13.3080 | 1.62583 | 0.812917 | − | 0.582380i | \(-0.197879\pi\) | ||||
0.812917 | + | 0.582380i | \(0.197879\pi\) | |||||||
\(68\) | −5.72614 | −0.694396 | ||||||||
\(69\) | −1.43073 | −0.172239 | ||||||||
\(70\) | −3.55618 | −0.425045 | ||||||||
\(71\) | −0.440272 | −0.0522507 | −0.0261254 | − | 0.999659i | \(-0.508317\pi\) | ||||
−0.0261254 | + | 0.999659i | \(0.508317\pi\) | |||||||
\(72\) | 28.5928 | 3.36969 | ||||||||
\(73\) | 12.3438 | 1.44473 | 0.722364 | − | 0.691513i | \(-0.243056\pi\) | ||||
0.722364 | + | 0.691513i | \(0.243056\pi\) | |||||||
\(74\) | −31.2566 | −3.63350 | ||||||||
\(75\) | 2.19439 | 0.253387 | ||||||||
\(76\) | −10.9907 | −1.26072 | ||||||||
\(77\) | 1.78399 | 0.203304 | ||||||||
\(78\) | −3.60841 | −0.408572 | ||||||||
\(79\) | 14.4491 | 1.62565 | 0.812823 | − | 0.582511i | \(-0.197930\pi\) | ||||
0.812823 | + | 0.582511i | \(0.197930\pi\) | |||||||
\(80\) | −12.4328 | −1.39003 | ||||||||
\(81\) | 6.90344 | 0.767049 | ||||||||
\(82\) | −13.2343 | −1.46148 | ||||||||
\(83\) | −2.65016 | −0.290893 | −0.145447 | − | 0.989366i | \(-0.546462\pi\) | ||||
−0.145447 | + | 0.989366i | \(0.546462\pi\) | |||||||
\(84\) | 4.99733 | 0.545253 | ||||||||
\(85\) | 0.717152 | 0.0777860 | ||||||||
\(86\) | 2.77959 | 0.299731 | ||||||||
\(87\) | −1.65063 | −0.176966 | ||||||||
\(88\) | 10.3571 | 1.10407 | ||||||||
\(89\) | −16.2884 | −1.72657 | −0.863284 | − | 0.504718i | \(-0.831597\pi\) | ||||
−0.863284 | + | 0.504718i | \(0.831597\pi\) | |||||||
\(90\) | −5.50312 | −0.580080 | ||||||||
\(91\) | 4.73414 | 0.496272 | ||||||||
\(92\) | 16.7469 | 1.74598 | ||||||||
\(93\) | 1.25238 | 0.129866 | ||||||||
\(94\) | 1.27106 | 0.131100 | ||||||||
\(95\) | 1.37650 | 0.141226 | ||||||||
\(96\) | 13.4401 | 1.37172 | ||||||||
\(97\) | 18.0088 | 1.82852 | 0.914258 | − | 0.405133i | \(-0.132775\pi\) | ||||
0.914258 | + | 0.405133i | \(0.132775\pi\) | |||||||
\(98\) | 10.6108 | 1.07185 | ||||||||
\(99\) | 2.76069 | 0.277459 | ||||||||
\(100\) | −25.6857 | −2.56857 | ||||||||
\(101\) | −10.5009 | −1.04488 | −0.522439 | − | 0.852677i | \(-0.674978\pi\) | ||||
−0.522439 | + | 0.852677i | \(0.674978\pi\) | |||||||
\(102\) | −1.35977 | −0.134637 | ||||||||
\(103\) | 17.7249 | 1.74649 | 0.873245 | − | 0.487282i | \(-0.162012\pi\) | ||||
0.873245 | + | 0.487282i | \(0.162012\pi\) | |||||||
\(104\) | 27.4846 | 2.69509 | ||||||||
\(105\) | −0.625875 | −0.0610791 | ||||||||
\(106\) | 14.6665 | 1.42454 | ||||||||
\(107\) | 3.80869 | 0.368200 | 0.184100 | − | 0.982907i | \(-0.441063\pi\) | ||||
0.184100 | + | 0.982907i | \(0.441063\pi\) | |||||||
\(108\) | 16.1369 | 1.55278 | ||||||||
\(109\) | 5.32049 | 0.509610 | 0.254805 | − | 0.966992i | \(-0.417989\pi\) | ||||
0.254805 | + | 0.966992i | \(0.417989\pi\) | |||||||
\(110\) | −1.99339 | −0.190062 | ||||||||
\(111\) | −5.50104 | −0.522136 | ||||||||
\(112\) | −30.9278 | −2.92240 | ||||||||
\(113\) | 9.54212 | 0.897647 | 0.448824 | − | 0.893620i | \(-0.351843\pi\) | ||||
0.448824 | + | 0.893620i | \(0.351843\pi\) | |||||||
\(114\) | −2.60994 | −0.244443 | ||||||||
\(115\) | −2.09741 | −0.195584 | ||||||||
\(116\) | 19.3209 | 1.79390 | ||||||||
\(117\) | 7.32599 | 0.677288 | ||||||||
\(118\) | 3.51071 | 0.323187 | ||||||||
\(119\) | 1.78399 | 0.163538 | ||||||||
\(120\) | −3.63359 | −0.331700 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 38.5811 | 3.49297 | ||||||||
\(123\) | −2.32918 | −0.210015 | ||||||||
\(124\) | −14.6593 | −1.31644 | ||||||||
\(125\) | 6.80268 | 0.608450 | ||||||||
\(126\) | −13.6896 | −1.21956 | ||||||||
\(127\) | 15.1289 | 1.34247 | 0.671236 | − | 0.741244i | \(-0.265764\pi\) | ||||
0.671236 | + | 0.741244i | \(0.265764\pi\) | |||||||
\(128\) | −60.9423 | −5.38659 | ||||||||
\(129\) | 0.489198 | 0.0430715 | ||||||||
\(130\) | −5.28983 | −0.463949 | ||||||||
\(131\) | −5.60889 | −0.490051 | −0.245025 | − | 0.969517i | \(-0.578796\pi\) | ||||
−0.245025 | + | 0.969517i | \(0.578796\pi\) | |||||||
\(132\) | 2.80122 | 0.243814 | ||||||||
\(133\) | 3.42417 | 0.296913 | ||||||||
\(134\) | −36.9909 | −3.19552 | ||||||||
\(135\) | −2.02102 | −0.173941 | ||||||||
\(136\) | 10.3571 | 0.888117 | ||||||||
\(137\) | −2.41469 | −0.206300 | −0.103150 | − | 0.994666i | \(-0.532892\pi\) | ||||
−0.103150 | + | 0.994666i | \(0.532892\pi\) | |||||||
\(138\) | 3.97684 | 0.338531 | ||||||||
\(139\) | 2.64721 | 0.224533 | 0.112267 | − | 0.993678i | \(-0.464189\pi\) | ||||
0.112267 | + | 0.993678i | \(0.464189\pi\) | |||||||
\(140\) | 7.32595 | 0.619156 | ||||||||
\(141\) | 0.223702 | 0.0188391 | ||||||||
\(142\) | 1.22378 | 0.102697 | ||||||||
\(143\) | 2.65369 | 0.221912 | ||||||||
\(144\) | −47.8602 | −3.98835 | ||||||||
\(145\) | −2.41978 | −0.200952 | ||||||||
\(146\) | −34.3106 | −2.83957 | ||||||||
\(147\) | 1.86746 | 0.154026 | ||||||||
\(148\) | 64.3905 | 5.29286 | ||||||||
\(149\) | −12.1443 | −0.994897 | −0.497448 | − | 0.867494i | \(-0.665730\pi\) | ||||
−0.497448 | + | 0.867494i | \(0.665730\pi\) | |||||||
\(150\) | −6.09952 | −0.498024 | ||||||||
\(151\) | −14.1516 | −1.15164 | −0.575819 | − | 0.817577i | \(-0.695317\pi\) | ||||
−0.575819 | + | 0.817577i | \(0.695317\pi\) | |||||||
\(152\) | 19.8794 | 1.61243 | ||||||||
\(153\) | 2.76069 | 0.223188 | ||||||||
\(154\) | −4.95875 | −0.399588 | ||||||||
\(155\) | 1.83596 | 0.147468 | ||||||||
\(156\) | 7.43354 | 0.595160 | ||||||||
\(157\) | −8.32117 | −0.664102 | −0.332051 | − | 0.943261i | \(-0.607741\pi\) | ||||
−0.332051 | + | 0.943261i | \(0.607741\pi\) | |||||||
\(158\) | −40.1625 | −3.19516 | ||||||||
\(159\) | 2.58126 | 0.204707 | ||||||||
\(160\) | 19.7028 | 1.55765 | ||||||||
\(161\) | −5.21751 | −0.411197 | ||||||||
\(162\) | −19.1887 | −1.50761 | ||||||||
\(163\) | 17.4759 | 1.36882 | 0.684409 | − | 0.729098i | \(-0.260060\pi\) | ||||
0.684409 | + | 0.729098i | \(0.260060\pi\) | |||||||
\(164\) | 27.2634 | 2.12892 | ||||||||
\(165\) | −0.350829 | −0.0273120 | ||||||||
\(166\) | 7.36637 | 0.571741 | ||||||||
\(167\) | −21.7669 | −1.68437 | −0.842187 | − | 0.539185i | \(-0.818732\pi\) | ||||
−0.842187 | + | 0.539185i | \(0.818732\pi\) | |||||||
\(168\) | −9.03891 | −0.697367 | ||||||||
\(169\) | −5.95796 | −0.458304 | ||||||||
\(170\) | −1.99339 | −0.152886 | ||||||||
\(171\) | 5.29884 | 0.405213 | ||||||||
\(172\) | −5.72614 | −0.436614 | ||||||||
\(173\) | 24.5890 | 1.86947 | 0.934734 | − | 0.355348i | \(-0.115638\pi\) | ||||
0.934734 | + | 0.355348i | \(0.115638\pi\) | |||||||
\(174\) | 4.58808 | 0.347822 | ||||||||
\(175\) | 8.00241 | 0.604926 | ||||||||
\(176\) | −17.3364 | −1.30678 | ||||||||
\(177\) | 0.617872 | 0.0464421 | ||||||||
\(178\) | 45.2752 | 3.39352 | ||||||||
\(179\) | 13.5365 | 1.01176 | 0.505881 | − | 0.862603i | \(-0.331167\pi\) | ||||
0.505881 | + | 0.862603i | \(0.331167\pi\) | |||||||
\(180\) | 11.3368 | 0.844993 | ||||||||
\(181\) | 3.66616 | 0.272503 | 0.136252 | − | 0.990674i | \(-0.456494\pi\) | ||||
0.136252 | + | 0.990674i | \(0.456494\pi\) | |||||||
\(182\) | −13.1590 | −0.975408 | ||||||||
\(183\) | 6.79014 | 0.501941 | ||||||||
\(184\) | −30.2908 | −2.23307 | ||||||||
\(185\) | −8.06438 | −0.592905 | ||||||||
\(186\) | −3.48111 | −0.255247 | ||||||||
\(187\) | 1.00000 | 0.0731272 | ||||||||
\(188\) | −2.61846 | −0.190971 | ||||||||
\(189\) | −5.02748 | −0.365695 | ||||||||
\(190\) | −3.82610 | −0.277574 | ||||||||
\(191\) | 16.5546 | 1.19785 | 0.598924 | − | 0.800806i | \(-0.295595\pi\) | ||||
0.598924 | + | 0.800806i | \(0.295595\pi\) | |||||||
\(192\) | −20.3962 | −1.47197 | ||||||||
\(193\) | −15.4859 | −1.11470 | −0.557350 | − | 0.830278i | \(-0.688182\pi\) | ||||
−0.557350 | + | 0.830278i | \(0.688182\pi\) | |||||||
\(194\) | −50.0571 | −3.59389 | ||||||||
\(195\) | −0.930990 | −0.0666696 | ||||||||
\(196\) | −21.8589 | −1.56135 | ||||||||
\(197\) | −1.46484 | −0.104365 | −0.0521826 | − | 0.998638i | \(-0.516618\pi\) | ||||
−0.0521826 | + | 0.998638i | \(0.516618\pi\) | |||||||
\(198\) | −7.67358 | −0.545338 | ||||||||
\(199\) | −10.6094 | −0.752080 | −0.376040 | − | 0.926603i | \(-0.622715\pi\) | ||||
−0.376040 | + | 0.926603i | \(0.622715\pi\) | |||||||
\(200\) | 46.4590 | 3.28514 | ||||||||
\(201\) | −6.51026 | −0.459198 | ||||||||
\(202\) | 29.1882 | 2.05367 | ||||||||
\(203\) | −6.01945 | −0.422482 | ||||||||
\(204\) | 2.80122 | 0.196124 | ||||||||
\(205\) | −3.41452 | −0.238480 | ||||||||
\(206\) | −49.2681 | −3.43267 | ||||||||
\(207\) | −8.07400 | −0.561181 | ||||||||
\(208\) | −46.0052 | −3.18989 | ||||||||
\(209\) | 1.91939 | 0.132767 | ||||||||
\(210\) | 1.73968 | 0.120049 | ||||||||
\(211\) | −8.01027 | −0.551450 | −0.275725 | − | 0.961237i | \(-0.588918\pi\) | ||||
−0.275725 | + | 0.961237i | \(0.588918\pi\) | |||||||
\(212\) | −30.2140 | −2.07511 | ||||||||
\(213\) | 0.215380 | 0.0147576 | ||||||||
\(214\) | −10.5866 | −0.723686 | ||||||||
\(215\) | 0.717152 | 0.0489093 | ||||||||
\(216\) | −29.1876 | −1.98597 | ||||||||
\(217\) | 4.56712 | 0.310037 | ||||||||
\(218\) | −14.7888 | −1.00162 | ||||||||
\(219\) | −6.03854 | −0.408047 | ||||||||
\(220\) | 4.10651 | 0.276861 | ||||||||
\(221\) | 2.65369 | 0.178506 | ||||||||
\(222\) | 15.2907 | 1.02624 | ||||||||
\(223\) | −11.3710 | −0.761457 | −0.380728 | − | 0.924687i | \(-0.624327\pi\) | ||||
−0.380728 | + | 0.924687i | \(0.624327\pi\) | |||||||
\(224\) | 49.0128 | 3.27480 | ||||||||
\(225\) | 12.3836 | 0.825572 | ||||||||
\(226\) | −26.5232 | −1.76430 | ||||||||
\(227\) | −14.7188 | −0.976922 | −0.488461 | − | 0.872586i | \(-0.662441\pi\) | ||||
−0.488461 | + | 0.872586i | \(0.662441\pi\) | |||||||
\(228\) | 5.37664 | 0.356076 | ||||||||
\(229\) | 15.6185 | 1.03210 | 0.516050 | − | 0.856558i | \(-0.327402\pi\) | ||||
0.516050 | + | 0.856558i | \(0.327402\pi\) | |||||||
\(230\) | 5.82994 | 0.384415 | ||||||||
\(231\) | −0.872723 | −0.0574209 | ||||||||
\(232\) | −34.9466 | −2.29436 | ||||||||
\(233\) | −20.5061 | −1.34340 | −0.671700 | − | 0.740824i | \(-0.734435\pi\) | ||||
−0.671700 | + | 0.740824i | \(0.734435\pi\) | |||||||
\(234\) | −20.3633 | −1.33119 | ||||||||
\(235\) | 0.327941 | 0.0213925 | ||||||||
\(236\) | −7.23228 | −0.470781 | ||||||||
\(237\) | −7.06845 | −0.459145 | ||||||||
\(238\) | −4.95875 | −0.321428 | ||||||||
\(239\) | −27.1275 | −1.75473 | −0.877367 | − | 0.479819i | \(-0.840702\pi\) | ||||
−0.877367 | + | 0.479819i | \(0.840702\pi\) | |||||||
\(240\) | 6.08210 | 0.392598 | ||||||||
\(241\) | 19.5058 | 1.25648 | 0.628240 | − | 0.778020i | \(-0.283776\pi\) | ||||
0.628240 | + | 0.778020i | \(0.283776\pi\) | |||||||
\(242\) | −2.77959 | −0.178679 | ||||||||
\(243\) | −11.8315 | −0.758991 | ||||||||
\(244\) | −79.4795 | −5.08816 | ||||||||
\(245\) | 2.73765 | 0.174902 | ||||||||
\(246\) | 6.47418 | 0.412779 | ||||||||
\(247\) | 5.09347 | 0.324090 | ||||||||
\(248\) | 26.5150 | 1.68370 | ||||||||
\(249\) | 1.29646 | 0.0821595 | ||||||||
\(250\) | −18.9087 | −1.19589 | ||||||||
\(251\) | −11.4796 | −0.724588 | −0.362294 | − | 0.932064i | \(-0.618006\pi\) | ||||
−0.362294 | + | 0.932064i | \(0.618006\pi\) | |||||||
\(252\) | 28.2014 | 1.77652 | ||||||||
\(253\) | −2.92463 | −0.183870 | ||||||||
\(254\) | −42.0521 | −2.63859 | ||||||||
\(255\) | −0.350829 | −0.0219698 | ||||||||
\(256\) | 86.0086 | 5.37554 | ||||||||
\(257\) | −10.9675 | −0.684132 | −0.342066 | − | 0.939676i | \(-0.611127\pi\) | ||||
−0.342066 | + | 0.939676i | \(0.611127\pi\) | |||||||
\(258\) | −1.35977 | −0.0846557 | ||||||||
\(259\) | −20.0609 | −1.24653 | ||||||||
\(260\) | 10.8974 | 0.675827 | ||||||||
\(261\) | −9.31498 | −0.576583 | ||||||||
\(262\) | 15.5904 | 0.963180 | ||||||||
\(263\) | −14.5632 | −0.898006 | −0.449003 | − | 0.893530i | \(-0.648221\pi\) | ||||
−0.449003 | + | 0.893530i | \(0.648221\pi\) | |||||||
\(264\) | −5.06669 | −0.311833 | ||||||||
\(265\) | 3.78406 | 0.232453 | ||||||||
\(266\) | −9.51780 | −0.583574 | ||||||||
\(267\) | 7.96826 | 0.487650 | ||||||||
\(268\) | 76.2035 | 4.65487 | ||||||||
\(269\) | 21.0459 | 1.28319 | 0.641595 | − | 0.767044i | \(-0.278273\pi\) | ||||
0.641595 | + | 0.767044i | \(0.278273\pi\) | |||||||
\(270\) | 5.61760 | 0.341877 | ||||||||
\(271\) | −17.0256 | −1.03423 | −0.517117 | − | 0.855915i | \(-0.672995\pi\) | ||||
−0.517117 | + | 0.855915i | \(0.672995\pi\) | |||||||
\(272\) | −17.3364 | −1.05117 | ||||||||
\(273\) | −2.31593 | −0.140167 | ||||||||
\(274\) | 6.71184 | 0.405477 | ||||||||
\(275\) | 4.48569 | 0.270497 | ||||||||
\(276\) | −8.19253 | −0.493132 | ||||||||
\(277\) | −7.33517 | −0.440728 | −0.220364 | − | 0.975418i | \(-0.570724\pi\) | ||||
−0.220364 | + | 0.975418i | \(0.570724\pi\) | |||||||
\(278\) | −7.35816 | −0.441313 | ||||||||
\(279\) | 7.06754 | 0.423123 | ||||||||
\(280\) | −13.2508 | −0.791887 | ||||||||
\(281\) | −5.45211 | −0.325246 | −0.162623 | − | 0.986688i | \(-0.551995\pi\) | ||||
−0.162623 | + | 0.986688i | \(0.551995\pi\) | |||||||
\(282\) | −0.621799 | −0.0370276 | ||||||||
\(283\) | −9.33787 | −0.555079 | −0.277539 | − | 0.960714i | \(-0.589519\pi\) | ||||
−0.277539 | + | 0.960714i | \(0.589519\pi\) | |||||||
\(284\) | −2.52106 | −0.149597 | ||||||||
\(285\) | −0.673380 | −0.0398876 | ||||||||
\(286\) | −7.37616 | −0.436162 | ||||||||
\(287\) | −8.49396 | −0.501383 | ||||||||
\(288\) | 75.8463 | 4.46929 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 6.72601 | 0.394965 | ||||||||
\(291\) | −8.80987 | −0.516444 | ||||||||
\(292\) | 70.6820 | 4.13635 | ||||||||
\(293\) | 5.39843 | 0.315380 | 0.157690 | − | 0.987489i | \(-0.449595\pi\) | ||||
0.157690 | + | 0.987489i | \(0.449595\pi\) | |||||||
\(294\) | −5.19078 | −0.302733 | ||||||||
\(295\) | 0.905783 | 0.0527368 | ||||||||
\(296\) | −116.466 | −6.76946 | ||||||||
\(297\) | −2.81812 | −0.163524 | ||||||||
\(298\) | 33.7561 | 1.95544 | ||||||||
\(299\) | −7.76106 | −0.448834 | ||||||||
\(300\) | 12.5654 | 0.725463 | ||||||||
\(301\) | 1.78399 | 0.102827 | ||||||||
\(302\) | 39.3356 | 2.26351 | ||||||||
\(303\) | 5.13702 | 0.295114 | ||||||||
\(304\) | −33.2753 | −1.90847 | ||||||||
\(305\) | 9.95416 | 0.569974 | ||||||||
\(306\) | −7.67358 | −0.438669 | ||||||||
\(307\) | 23.0994 | 1.31835 | 0.659175 | − | 0.751989i | \(-0.270906\pi\) | ||||
0.659175 | + | 0.751989i | \(0.270906\pi\) | |||||||
\(308\) | 10.2153 | 0.582073 | ||||||||
\(309\) | −8.67100 | −0.493276 | ||||||||
\(310\) | −5.10321 | −0.289843 | ||||||||
\(311\) | 19.3785 | 1.09885 | 0.549426 | − | 0.835542i | \(-0.314846\pi\) | ||||
0.549426 | + | 0.835542i | \(0.314846\pi\) | |||||||
\(312\) | −13.4454 | −0.761196 | ||||||||
\(313\) | 25.4255 | 1.43714 | 0.718568 | − | 0.695456i | \(-0.244798\pi\) | ||||
0.718568 | + | 0.695456i | \(0.244798\pi\) | |||||||
\(314\) | 23.1295 | 1.30527 | ||||||||
\(315\) | −3.53199 | −0.199005 | ||||||||
\(316\) | 82.7373 | 4.65433 | ||||||||
\(317\) | −26.8607 | −1.50865 | −0.754324 | − | 0.656502i | \(-0.772035\pi\) | ||||
−0.754324 | + | 0.656502i | \(0.772035\pi\) | |||||||
\(318\) | −7.17484 | −0.402345 | ||||||||
\(319\) | −3.37416 | −0.188916 | ||||||||
\(320\) | −29.9003 | −1.67148 | ||||||||
\(321\) | −1.86321 | −0.103994 | ||||||||
\(322\) | 14.5025 | 0.808195 | ||||||||
\(323\) | 1.91939 | 0.106798 | ||||||||
\(324\) | 39.5300 | 2.19611 | ||||||||
\(325\) | 11.9036 | 0.660294 | ||||||||
\(326\) | −48.5759 | −2.69037 | ||||||||
\(327\) | −2.60277 | −0.143934 | ||||||||
\(328\) | −49.3127 | −2.72284 | ||||||||
\(329\) | 0.815785 | 0.0449757 | ||||||||
\(330\) | 0.975163 | 0.0536809 | ||||||||
\(331\) | 5.04191 | 0.277129 | 0.138564 | − | 0.990353i | \(-0.455751\pi\) | ||||
0.138564 | + | 0.990353i | \(0.455751\pi\) | |||||||
\(332\) | −15.1752 | −0.832847 | ||||||||
\(333\) | −31.0439 | −1.70120 | ||||||||
\(334\) | 60.5032 | 3.31059 | ||||||||
\(335\) | −9.54387 | −0.521437 | ||||||||
\(336\) | 15.1298 | 0.825400 | ||||||||
\(337\) | 22.4238 | 1.22150 | 0.610752 | − | 0.791822i | \(-0.290867\pi\) | ||||
0.610752 | + | 0.791822i | \(0.290867\pi\) | |||||||
\(338\) | 16.5607 | 0.900783 | ||||||||
\(339\) | −4.66799 | −0.253530 | ||||||||
\(340\) | 4.10651 | 0.222707 | ||||||||
\(341\) | 2.56007 | 0.138635 | ||||||||
\(342\) | −14.7286 | −0.796433 | ||||||||
\(343\) | 19.2981 | 1.04200 | ||||||||
\(344\) | 10.3571 | 0.558420 | ||||||||
\(345\) | 1.02605 | 0.0552405 | ||||||||
\(346\) | −68.3475 | −3.67438 | ||||||||
\(347\) | 31.7997 | 1.70710 | 0.853548 | − | 0.521015i | \(-0.174446\pi\) | ||||
0.853548 | + | 0.521015i | \(0.174446\pi\) | |||||||
\(348\) | −9.45174 | −0.506666 | ||||||||
\(349\) | 32.7078 | 1.75081 | 0.875404 | − | 0.483392i | \(-0.160595\pi\) | ||||
0.875404 | + | 0.483392i | \(0.160595\pi\) | |||||||
\(350\) | −22.2435 | −1.18896 | ||||||||
\(351\) | −7.47839 | −0.399167 | ||||||||
\(352\) | 27.4737 | 1.46435 | ||||||||
\(353\) | 1.49905 | 0.0797864 | 0.0398932 | − | 0.999204i | \(-0.487298\pi\) | ||||
0.0398932 | + | 0.999204i | \(0.487298\pi\) | |||||||
\(354\) | −1.71743 | −0.0912804 | ||||||||
\(355\) | 0.315742 | 0.0167578 | ||||||||
\(356\) | −93.2697 | −4.94328 | ||||||||
\(357\) | −0.872723 | −0.0461894 | ||||||||
\(358\) | −37.6258 | −1.98859 | ||||||||
\(359\) | −21.4632 | −1.13279 | −0.566393 | − | 0.824135i | \(-0.691662\pi\) | ||||
−0.566393 | + | 0.824135i | \(0.691662\pi\) | |||||||
\(360\) | −20.5054 | −1.08073 | ||||||||
\(361\) | −15.3159 | −0.806101 | ||||||||
\(362\) | −10.1904 | −0.535597 | ||||||||
\(363\) | −0.489198 | −0.0256762 | ||||||||
\(364\) | 27.1083 | 1.42086 | ||||||||
\(365\) | −8.85235 | −0.463353 | ||||||||
\(366\) | −18.8738 | −0.986550 | ||||||||
\(367\) | 11.9337 | 0.622937 | 0.311468 | − | 0.950257i | \(-0.399179\pi\) | ||||
0.311468 | + | 0.950257i | \(0.399179\pi\) | |||||||
\(368\) | 50.7025 | 2.64305 | ||||||||
\(369\) | −13.1442 | −0.684262 | ||||||||
\(370\) | 22.4157 | 1.16534 | ||||||||
\(371\) | 9.41321 | 0.488710 | ||||||||
\(372\) | 7.17130 | 0.371815 | ||||||||
\(373\) | 16.7645 | 0.868033 | 0.434016 | − | 0.900905i | \(-0.357096\pi\) | ||||
0.434016 | + | 0.900905i | \(0.357096\pi\) | |||||||
\(374\) | −2.77959 | −0.143729 | ||||||||
\(375\) | −3.32786 | −0.171850 | ||||||||
\(376\) | 4.73613 | 0.244247 | ||||||||
\(377\) | −8.95395 | −0.461152 | ||||||||
\(378\) | 13.9743 | 0.718763 | ||||||||
\(379\) | −16.0006 | −0.821897 | −0.410949 | − | 0.911659i | \(-0.634802\pi\) | ||||
−0.410949 | + | 0.911659i | \(0.634802\pi\) | |||||||
\(380\) | 7.88201 | 0.404338 | ||||||||
\(381\) | −7.40102 | −0.379166 | ||||||||
\(382\) | −46.0150 | −2.35433 | ||||||||
\(383\) | −15.7420 | −0.804381 | −0.402190 | − | 0.915556i | \(-0.631751\pi\) | ||||
−0.402190 | + | 0.915556i | \(0.631751\pi\) | |||||||
\(384\) | 29.8129 | 1.52138 | ||||||||
\(385\) | −1.27939 | −0.0652037 | ||||||||
\(386\) | 43.0445 | 2.19091 | ||||||||
\(387\) | 2.76069 | 0.140334 | ||||||||
\(388\) | 103.121 | 5.23516 | ||||||||
\(389\) | −29.8938 | −1.51567 | −0.757837 | − | 0.652444i | \(-0.773744\pi\) | ||||
−0.757837 | + | 0.652444i | \(0.773744\pi\) | |||||||
\(390\) | 2.58777 | 0.131037 | ||||||||
\(391\) | −2.92463 | −0.147905 | ||||||||
\(392\) | 39.5373 | 1.99693 | ||||||||
\(393\) | 2.74386 | 0.138409 | ||||||||
\(394\) | 4.07165 | 0.205127 | ||||||||
\(395\) | −10.3622 | −0.521377 | ||||||||
\(396\) | 15.8081 | 0.794385 | ||||||||
\(397\) | 15.3964 | 0.772722 | 0.386361 | − | 0.922348i | \(-0.373732\pi\) | ||||
0.386361 | + | 0.922348i | \(0.373732\pi\) | |||||||
\(398\) | 29.4898 | 1.47819 | ||||||||
\(399\) | −1.67510 | −0.0838598 | ||||||||
\(400\) | −77.7656 | −3.88828 | ||||||||
\(401\) | 9.36974 | 0.467902 | 0.233951 | − | 0.972248i | \(-0.424834\pi\) | ||||
0.233951 | + | 0.972248i | \(0.424834\pi\) | |||||||
\(402\) | 18.0959 | 0.902540 | ||||||||
\(403\) | 6.79361 | 0.338414 | ||||||||
\(404\) | −60.1295 | −2.99156 | ||||||||
\(405\) | −4.95081 | −0.246008 | ||||||||
\(406\) | 16.7316 | 0.830376 | ||||||||
\(407\) | −11.2450 | −0.557395 | ||||||||
\(408\) | −5.06669 | −0.250839 | ||||||||
\(409\) | −8.89437 | −0.439798 | −0.219899 | − | 0.975523i | \(-0.570573\pi\) | ||||
−0.219899 | + | 0.975523i | \(0.570573\pi\) | |||||||
\(410\) | 9.49098 | 0.468726 | ||||||||
\(411\) | 1.18126 | 0.0582672 | ||||||||
\(412\) | 101.495 | 5.00032 | ||||||||
\(413\) | 2.25323 | 0.110874 | ||||||||
\(414\) | 22.4424 | 1.10298 | ||||||||
\(415\) | 1.90057 | 0.0932953 | ||||||||
\(416\) | 72.9066 | 3.57454 | ||||||||
\(417\) | −1.29501 | −0.0634169 | ||||||||
\(418\) | −5.33513 | −0.260950 | ||||||||
\(419\) | 3.13764 | 0.153284 | 0.0766419 | − | 0.997059i | \(-0.475580\pi\) | ||||
0.0766419 | + | 0.997059i | \(0.475580\pi\) | |||||||
\(420\) | −3.58384 | −0.174874 | ||||||||
\(421\) | 11.8913 | 0.579549 | 0.289774 | − | 0.957095i | \(-0.406420\pi\) | ||||
0.289774 | + | 0.957095i | \(0.406420\pi\) | |||||||
\(422\) | 22.2653 | 1.08386 | ||||||||
\(423\) | 1.26241 | 0.0613806 | ||||||||
\(424\) | 54.6495 | 2.65401 | ||||||||
\(425\) | 4.48569 | 0.217588 | ||||||||
\(426\) | −0.598670 | −0.0290056 | ||||||||
\(427\) | 24.7620 | 1.19832 | ||||||||
\(428\) | 21.8091 | 1.05418 | ||||||||
\(429\) | −1.29818 | −0.0626766 | ||||||||
\(430\) | −1.99339 | −0.0961298 | ||||||||
\(431\) | 9.04070 | 0.435475 | 0.217738 | − | 0.976007i | \(-0.430132\pi\) | ||||
0.217738 | + | 0.976007i | \(0.430132\pi\) | |||||||
\(432\) | 48.8559 | 2.35058 | ||||||||
\(433\) | −34.6003 | −1.66278 | −0.831392 | − | 0.555686i | \(-0.812456\pi\) | ||||
−0.831392 | + | 0.555686i | \(0.812456\pi\) | |||||||
\(434\) | −12.6947 | −0.609367 | ||||||||
\(435\) | 1.18375 | 0.0567566 | ||||||||
\(436\) | 30.4658 | 1.45905 | ||||||||
\(437\) | −5.61353 | −0.268531 | ||||||||
\(438\) | 16.7847 | 0.802004 | ||||||||
\(439\) | 24.2461 | 1.15720 | 0.578601 | − | 0.815610i | \(-0.303599\pi\) | ||||
0.578601 | + | 0.815610i | \(0.303599\pi\) | |||||||
\(440\) | −7.42764 | −0.354099 | ||||||||
\(441\) | 10.5386 | 0.501839 | ||||||||
\(442\) | −7.37616 | −0.350848 | ||||||||
\(443\) | −22.9778 | −1.09171 | −0.545855 | − | 0.837880i | \(-0.683795\pi\) | ||||
−0.545855 | + | 0.837880i | \(0.683795\pi\) | |||||||
\(444\) | −31.4997 | −1.49491 | ||||||||
\(445\) | 11.6813 | 0.553745 | ||||||||
\(446\) | 31.6067 | 1.49662 | ||||||||
\(447\) | 5.94095 | 0.280997 | ||||||||
\(448\) | −74.3799 | −3.51412 | ||||||||
\(449\) | −19.0000 | −0.896665 | −0.448332 | − | 0.893867i | \(-0.647982\pi\) | ||||
−0.448332 | + | 0.893867i | \(0.647982\pi\) | |||||||
\(450\) | −34.4213 | −1.62264 | ||||||||
\(451\) | −4.76123 | −0.224197 | ||||||||
\(452\) | 54.6395 | 2.57002 | ||||||||
\(453\) | 6.92292 | 0.325267 | ||||||||
\(454\) | 40.9123 | 1.92011 | ||||||||
\(455\) | −3.39509 | −0.159164 | ||||||||
\(456\) | −9.72498 | −0.455414 | ||||||||
\(457\) | 5.86527 | 0.274366 | 0.137183 | − | 0.990546i | \(-0.456195\pi\) | ||||
0.137183 | + | 0.990546i | \(0.456195\pi\) | |||||||
\(458\) | −43.4131 | −2.02856 | ||||||||
\(459\) | −2.81812 | −0.131538 | ||||||||
\(460\) | −12.0100 | −0.559971 | ||||||||
\(461\) | 23.2379 | 1.08230 | 0.541148 | − | 0.840928i | \(-0.317990\pi\) | ||||
0.541148 | + | 0.840928i | \(0.317990\pi\) | |||||||
\(462\) | 2.42581 | 0.112859 | ||||||||
\(463\) | −31.9003 | −1.48253 | −0.741267 | − | 0.671210i | \(-0.765775\pi\) | ||||
−0.741267 | + | 0.671210i | \(0.765775\pi\) | |||||||
\(464\) | 58.4956 | 2.71559 | ||||||||
\(465\) | −0.898147 | −0.0416506 | ||||||||
\(466\) | 56.9986 | 2.64041 | ||||||||
\(467\) | 11.8036 | 0.546203 | 0.273102 | − | 0.961985i | \(-0.411950\pi\) | ||||
0.273102 | + | 0.961985i | \(0.411950\pi\) | |||||||
\(468\) | 41.9496 | 1.93912 | ||||||||
\(469\) | −23.7413 | −1.09627 | ||||||||
\(470\) | −0.911541 | −0.0420463 | ||||||||
\(471\) | 4.07070 | 0.187568 | ||||||||
\(472\) | 13.0814 | 0.602119 | ||||||||
\(473\) | 1.00000 | 0.0459800 | ||||||||
\(474\) | 19.6474 | 0.902436 | ||||||||
\(475\) | 8.60981 | 0.395045 | ||||||||
\(476\) | 10.2153 | 0.468220 | ||||||||
\(477\) | 14.5668 | 0.666967 | ||||||||
\(478\) | 75.4035 | 3.44888 | ||||||||
\(479\) | 25.6936 | 1.17397 | 0.586985 | − | 0.809598i | \(-0.300315\pi\) | ||||
0.586985 | + | 0.809598i | \(0.300315\pi\) | |||||||
\(480\) | −9.63859 | −0.439939 | ||||||||
\(481\) | −29.8407 | −1.36062 | ||||||||
\(482\) | −54.2182 | −2.46957 | ||||||||
\(483\) | 2.55239 | 0.116138 | ||||||||
\(484\) | 5.72614 | 0.260279 | ||||||||
\(485\) | −12.9150 | −0.586441 | ||||||||
\(486\) | 32.8868 | 1.49177 | ||||||||
\(487\) | 18.7901 | 0.851460 | 0.425730 | − | 0.904850i | \(-0.360017\pi\) | ||||
0.425730 | + | 0.904850i | \(0.360017\pi\) | |||||||
\(488\) | 143.759 | 6.50764 | ||||||||
\(489\) | −8.54918 | −0.386607 | ||||||||
\(490\) | −7.60955 | −0.343765 | ||||||||
\(491\) | −0.735094 | −0.0331743 | −0.0165872 | − | 0.999862i | \(-0.505280\pi\) | ||||
−0.0165872 | + | 0.999862i | \(0.505280\pi\) | |||||||
\(492\) | −13.3372 | −0.601288 | ||||||||
\(493\) | −3.37416 | −0.151964 | ||||||||
\(494\) | −14.1578 | −0.636988 | ||||||||
\(495\) | −1.97983 | −0.0889867 | ||||||||
\(496\) | −44.3822 | −1.99282 | ||||||||
\(497\) | 0.785440 | 0.0352318 | ||||||||
\(498\) | −3.60362 | −0.161482 | ||||||||
\(499\) | −17.7973 | −0.796714 | −0.398357 | − | 0.917230i | \(-0.630420\pi\) | ||||
−0.398357 | + | 0.917230i | \(0.630420\pi\) | |||||||
\(500\) | 38.9531 | 1.74203 | ||||||||
\(501\) | 10.6483 | 0.475733 | ||||||||
\(502\) | 31.9087 | 1.42416 | ||||||||
\(503\) | 7.75317 | 0.345697 | 0.172848 | − | 0.984948i | \(-0.444703\pi\) | ||||
0.172848 | + | 0.984948i | \(0.444703\pi\) | |||||||
\(504\) | −51.0092 | −2.27213 | ||||||||
\(505\) | 7.53073 | 0.335113 | ||||||||
\(506\) | 8.12929 | 0.361391 | ||||||||
\(507\) | 2.91462 | 0.129443 | ||||||||
\(508\) | 86.6301 | 3.84359 | ||||||||
\(509\) | 25.8806 | 1.14714 | 0.573569 | − | 0.819158i | \(-0.305559\pi\) | ||||
0.573569 | + | 0.819158i | \(0.305559\pi\) | |||||||
\(510\) | 0.975163 | 0.0431809 | ||||||||
\(511\) | −22.0211 | −0.974156 | ||||||||
\(512\) | −117.184 | −5.17886 | ||||||||
\(513\) | −5.40908 | −0.238817 | ||||||||
\(514\) | 30.4851 | 1.34464 | ||||||||
\(515\) | −12.7115 | −0.560134 | ||||||||
\(516\) | 2.80122 | 0.123317 | ||||||||
\(517\) | 0.457282 | 0.0201112 | ||||||||
\(518\) | 55.7613 | 2.45001 | ||||||||
\(519\) | −12.0289 | −0.528010 | ||||||||
\(520\) | −19.7106 | −0.864368 | ||||||||
\(521\) | 20.7652 | 0.909740 | 0.454870 | − | 0.890558i | \(-0.349686\pi\) | ||||
0.454870 | + | 0.890558i | \(0.349686\pi\) | |||||||
\(522\) | 25.8919 | 1.13326 | ||||||||
\(523\) | −21.2531 | −0.929333 | −0.464666 | − | 0.885486i | \(-0.653826\pi\) | ||||
−0.464666 | + | 0.885486i | \(0.653826\pi\) | |||||||
\(524\) | −32.1173 | −1.40305 | ||||||||
\(525\) | −3.91477 | −0.170854 | ||||||||
\(526\) | 40.4798 | 1.76500 | ||||||||
\(527\) | 2.56007 | 0.111518 | ||||||||
\(528\) | 8.48091 | 0.369084 | ||||||||
\(529\) | −14.4465 | −0.628109 | ||||||||
\(530\) | −10.5181 | −0.456878 | ||||||||
\(531\) | 3.48683 | 0.151315 | ||||||||
\(532\) | 19.6073 | 0.850083 | ||||||||
\(533\) | −12.6348 | −0.547274 | ||||||||
\(534\) | −22.1485 | −0.958461 | ||||||||
\(535\) | −2.73141 | −0.118089 | ||||||||
\(536\) | −137.833 | −5.95348 | ||||||||
\(537\) | −6.62201 | −0.285761 | ||||||||
\(538\) | −58.4989 | −2.52207 | ||||||||
\(539\) | 3.81739 | 0.164427 | ||||||||
\(540\) | −11.5726 | −0.498006 | ||||||||
\(541\) | −23.3890 | −1.00557 | −0.502785 | − | 0.864412i | \(-0.667691\pi\) | ||||
−0.502785 | + | 0.864412i | \(0.667691\pi\) | |||||||
\(542\) | 47.3243 | 2.03275 | ||||||||
\(543\) | −1.79348 | −0.0769655 | ||||||||
\(544\) | 27.4737 | 1.17793 | ||||||||
\(545\) | −3.81560 | −0.163442 | ||||||||
\(546\) | 6.43735 | 0.275493 | ||||||||
\(547\) | −24.1858 | −1.03411 | −0.517054 | − | 0.855953i | \(-0.672972\pi\) | ||||
−0.517054 | + | 0.855953i | \(0.672972\pi\) | |||||||
\(548\) | −13.8268 | −0.590652 | ||||||||
\(549\) | 38.3187 | 1.63540 | ||||||||
\(550\) | −12.4684 | −0.531654 | ||||||||
\(551\) | −6.47633 | −0.275901 | ||||||||
\(552\) | 14.8182 | 0.630706 | ||||||||
\(553\) | −25.7769 | −1.09615 | ||||||||
\(554\) | 20.3888 | 0.866237 | ||||||||
\(555\) | 3.94508 | 0.167459 | ||||||||
\(556\) | 15.1583 | 0.642854 | ||||||||
\(557\) | −28.1891 | −1.19441 | −0.597205 | − | 0.802089i | \(-0.703722\pi\) | ||||
−0.597205 | + | 0.802089i | \(0.703722\pi\) | |||||||
\(558\) | −19.6449 | −0.831634 | ||||||||
\(559\) | 2.65369 | 0.112239 | ||||||||
\(560\) | 22.1799 | 0.937273 | ||||||||
\(561\) | −0.489198 | −0.0206540 | ||||||||
\(562\) | 15.1547 | 0.639261 | ||||||||
\(563\) | 21.4085 | 0.902260 | 0.451130 | − | 0.892458i | \(-0.351021\pi\) | ||||
0.451130 | + | 0.892458i | \(0.351021\pi\) | |||||||
\(564\) | 1.28095 | 0.0539375 | ||||||||
\(565\) | −6.84315 | −0.287893 | ||||||||
\(566\) | 25.9555 | 1.09099 | ||||||||
\(567\) | −12.3156 | −0.517208 | ||||||||
\(568\) | 4.55996 | 0.191332 | ||||||||
\(569\) | −36.9116 | −1.54741 | −0.773707 | − | 0.633544i | \(-0.781600\pi\) | ||||
−0.773707 | + | 0.633544i | \(0.781600\pi\) | |||||||
\(570\) | 1.87172 | 0.0783978 | ||||||||
\(571\) | −7.03740 | −0.294506 | −0.147253 | − | 0.989099i | \(-0.547043\pi\) | ||||
−0.147253 | + | 0.989099i | \(0.547043\pi\) | |||||||
\(572\) | 15.1954 | 0.635350 | ||||||||
\(573\) | −8.09847 | −0.338319 | ||||||||
\(574\) | 23.6097 | 0.985452 | ||||||||
\(575\) | −13.1190 | −0.547101 | ||||||||
\(576\) | −115.101 | −4.79589 | ||||||||
\(577\) | 22.6065 | 0.941122 | 0.470561 | − | 0.882367i | \(-0.344051\pi\) | ||||
0.470561 | + | 0.882367i | \(0.344051\pi\) | |||||||
\(578\) | −2.77959 | −0.115616 | ||||||||
\(579\) | 7.57567 | 0.314834 | ||||||||
\(580\) | −13.8560 | −0.575339 | ||||||||
\(581\) | 4.72785 | 0.196144 | ||||||||
\(582\) | 24.4878 | 1.01505 | ||||||||
\(583\) | 5.27651 | 0.218531 | ||||||||
\(584\) | −127.846 | −5.29031 | ||||||||
\(585\) | −5.25384 | −0.217220 | ||||||||
\(586\) | −15.0054 | −0.619869 | ||||||||
\(587\) | −15.9229 | −0.657209 | −0.328605 | − | 0.944468i | \(-0.606578\pi\) | ||||
−0.328605 | + | 0.944468i | \(0.606578\pi\) | |||||||
\(588\) | 10.6933 | 0.440986 | ||||||||
\(589\) | 4.91378 | 0.202469 | ||||||||
\(590\) | −2.51771 | −0.103652 | ||||||||
\(591\) | 0.716595 | 0.0294768 | ||||||||
\(592\) | 194.948 | 8.01230 | ||||||||
\(593\) | 13.0791 | 0.537095 | 0.268548 | − | 0.963266i | \(-0.413456\pi\) | ||||
0.268548 | + | 0.963266i | \(0.413456\pi\) | |||||||
\(594\) | 7.83322 | 0.321401 | ||||||||
\(595\) | −1.27939 | −0.0524498 | ||||||||
\(596\) | −69.5397 | −2.84846 | ||||||||
\(597\) | 5.19010 | 0.212417 | ||||||||
\(598\) | 21.5726 | 0.882169 | ||||||||
\(599\) | 38.6057 | 1.57739 | 0.788693 | − | 0.614787i | \(-0.210758\pi\) | ||||
0.788693 | + | 0.614787i | \(0.210758\pi\) | |||||||
\(600\) | −22.7276 | −0.927852 | ||||||||
\(601\) | −25.7237 | −1.04929 | −0.524645 | − | 0.851321i | \(-0.675802\pi\) | ||||
−0.524645 | + | 0.851321i | \(0.675802\pi\) | |||||||
\(602\) | −4.95875 | −0.202104 | ||||||||
\(603\) | −36.7392 | −1.49614 | ||||||||
\(604\) | −81.0337 | −3.29722 | ||||||||
\(605\) | −0.717152 | −0.0291564 | ||||||||
\(606\) | −14.2788 | −0.580037 | ||||||||
\(607\) | −13.3941 | −0.543648 | −0.271824 | − | 0.962347i | \(-0.587627\pi\) | ||||
−0.271824 | + | 0.962347i | \(0.587627\pi\) | |||||||
\(608\) | 52.7329 | 2.13860 | ||||||||
\(609\) | 2.94470 | 0.119325 | ||||||||
\(610\) | −27.6685 | −1.12027 | ||||||||
\(611\) | 1.21348 | 0.0490922 | ||||||||
\(612\) | 15.8081 | 0.639003 | ||||||||
\(613\) | −15.9231 | −0.643130 | −0.321565 | − | 0.946888i | \(-0.604209\pi\) | ||||
−0.321565 | + | 0.946888i | \(0.604209\pi\) | |||||||
\(614\) | −64.2068 | −2.59118 | ||||||||
\(615\) | 1.67038 | 0.0673561 | ||||||||
\(616\) | −18.4770 | −0.744459 | ||||||||
\(617\) | −2.60308 | −0.104796 | −0.0523981 | − | 0.998626i | \(-0.516686\pi\) | ||||
−0.0523981 | + | 0.998626i | \(0.516686\pi\) | |||||||
\(618\) | 24.1019 | 0.969519 | ||||||||
\(619\) | 26.8211 | 1.07803 | 0.539016 | − | 0.842296i | \(-0.318796\pi\) | ||||
0.539016 | + | 0.842296i | \(0.318796\pi\) | |||||||
\(620\) | 10.5129 | 0.422210 | ||||||||
\(621\) | 8.24196 | 0.330739 | ||||||||
\(622\) | −53.8643 | −2.15976 | ||||||||
\(623\) | 29.0583 | 1.16420 | ||||||||
\(624\) | 22.5057 | 0.900948 | ||||||||
\(625\) | 17.5499 | 0.701997 | ||||||||
\(626\) | −70.6727 | −2.82465 | ||||||||
\(627\) | −0.938964 | −0.0374986 | ||||||||
\(628\) | −47.6481 | −1.90137 | ||||||||
\(629\) | −11.2450 | −0.448368 | ||||||||
\(630\) | 9.81749 | 0.391138 | ||||||||
\(631\) | −41.5197 | −1.65287 | −0.826437 | − | 0.563028i | \(-0.809636\pi\) | ||||
−0.826437 | + | 0.563028i | \(0.809636\pi\) | |||||||
\(632\) | −149.651 | −5.95279 | ||||||||
\(633\) | 3.91861 | 0.155751 | ||||||||
\(634\) | 74.6618 | 2.96520 | ||||||||
\(635\) | −10.8497 | −0.430557 | ||||||||
\(636\) | 14.7806 | 0.586090 | ||||||||
\(637\) | 10.1302 | 0.401372 | ||||||||
\(638\) | 9.37878 | 0.371309 | ||||||||
\(639\) | 1.21545 | 0.0480826 | ||||||||
\(640\) | 43.7049 | 1.72759 | ||||||||
\(641\) | −7.92205 | −0.312902 | −0.156451 | − | 0.987686i | \(-0.550005\pi\) | ||||
−0.156451 | + | 0.987686i | \(0.550005\pi\) | |||||||
\(642\) | 5.17895 | 0.204397 | ||||||||
\(643\) | −40.0234 | −1.57837 | −0.789185 | − | 0.614156i | \(-0.789497\pi\) | ||||
−0.789185 | + | 0.614156i | \(0.789497\pi\) | |||||||
\(644\) | −29.8762 | −1.17729 | ||||||||
\(645\) | −0.350829 | −0.0138139 | ||||||||
\(646\) | −5.33513 | −0.209908 | ||||||||
\(647\) | 27.8331 | 1.09423 | 0.547116 | − | 0.837057i | \(-0.315726\pi\) | ||||
0.547116 | + | 0.837057i | \(0.315726\pi\) | |||||||
\(648\) | −71.4999 | −2.80878 | ||||||||
\(649\) | 1.26303 | 0.0495782 | ||||||||
\(650\) | −33.0872 | −1.29779 | ||||||||
\(651\) | −2.23423 | −0.0875664 | ||||||||
\(652\) | 100.069 | 3.91902 | ||||||||
\(653\) | −31.0691 | −1.21583 | −0.607914 | − | 0.794003i | \(-0.707994\pi\) | ||||
−0.607914 | + | 0.794003i | \(0.707994\pi\) | |||||||
\(654\) | 7.23465 | 0.282897 | ||||||||
\(655\) | 4.02242 | 0.157169 | ||||||||
\(656\) | 82.5423 | 3.22274 | ||||||||
\(657\) | −34.0772 | −1.32948 | ||||||||
\(658\) | −2.26755 | −0.0883983 | ||||||||
\(659\) | −39.3045 | −1.53109 | −0.765544 | − | 0.643384i | \(-0.777530\pi\) | ||||
−0.765544 | + | 0.643384i | \(0.777530\pi\) | |||||||
\(660\) | −2.00890 | −0.0781962 | ||||||||
\(661\) | −35.3330 | −1.37429 | −0.687147 | − | 0.726518i | \(-0.741137\pi\) | ||||
−0.687147 | + | 0.726518i | \(0.741137\pi\) | |||||||
\(662\) | −14.0145 | −0.544688 | ||||||||
\(663\) | −1.29818 | −0.0504171 | ||||||||
\(664\) | 27.4481 | 1.06519 | ||||||||
\(665\) | −2.45565 | −0.0952261 | ||||||||
\(666\) | 86.2895 | 3.34365 | ||||||||
\(667\) | 9.86817 | 0.382097 | ||||||||
\(668\) | −124.640 | −4.82248 | ||||||||
\(669\) | 5.56266 | 0.215065 | ||||||||
\(670\) | 26.5281 | 1.02487 | ||||||||
\(671\) | 13.8801 | 0.535837 | ||||||||
\(672\) | −23.9770 | −0.924931 | ||||||||
\(673\) | 3.13616 | 0.120890 | 0.0604451 | − | 0.998172i | \(-0.480748\pi\) | ||||
0.0604451 | + | 0.998172i | \(0.480748\pi\) | |||||||
\(674\) | −62.3291 | −2.40083 | ||||||||
\(675\) | −12.6412 | −0.486560 | ||||||||
\(676\) | −34.1161 | −1.31216 | ||||||||
\(677\) | −34.4738 | −1.32494 | −0.662468 | − | 0.749090i | \(-0.730491\pi\) | ||||
−0.662468 | + | 0.749090i | \(0.730491\pi\) | |||||||
\(678\) | 12.9751 | 0.498306 | ||||||||
\(679\) | −32.1274 | −1.23294 | ||||||||
\(680\) | −7.42764 | −0.284837 | ||||||||
\(681\) | 7.20042 | 0.275921 | ||||||||
\(682\) | −7.11595 | −0.272484 | ||||||||
\(683\) | −9.09626 | −0.348059 | −0.174029 | − | 0.984740i | \(-0.555679\pi\) | ||||
−0.174029 | + | 0.984740i | \(0.555679\pi\) | |||||||
\(684\) | 30.3419 | 1.16015 | ||||||||
\(685\) | 1.73170 | 0.0661647 | ||||||||
\(686\) | −53.6408 | −2.04802 | ||||||||
\(687\) | −7.64055 | −0.291505 | ||||||||
\(688\) | −17.3364 | −0.660942 | ||||||||
\(689\) | 14.0022 | 0.533441 | ||||||||
\(690\) | −2.85199 | −0.108574 | ||||||||
\(691\) | 18.0093 | 0.685108 | 0.342554 | − | 0.939498i | \(-0.388708\pi\) | ||||
0.342554 | + | 0.939498i | \(0.388708\pi\) | |||||||
\(692\) | 140.800 | 5.35241 | ||||||||
\(693\) | −4.92502 | −0.187086 | ||||||||
\(694\) | −88.3901 | −3.35524 | ||||||||
\(695\) | −1.89845 | −0.0720123 | ||||||||
\(696\) | 17.0958 | 0.648015 | ||||||||
\(697\) | −4.76123 | −0.180344 | ||||||||
\(698\) | −90.9144 | −3.44116 | ||||||||
\(699\) | 10.0315 | 0.379428 | ||||||||
\(700\) | 45.8229 | 1.73194 | ||||||||
\(701\) | 7.51648 | 0.283894 | 0.141947 | − | 0.989874i | \(-0.454664\pi\) | ||||
0.141947 | + | 0.989874i | \(0.454664\pi\) | |||||||
\(702\) | 20.7869 | 0.784551 | ||||||||
\(703\) | −21.5836 | −0.814041 | ||||||||
\(704\) | −41.6931 | −1.57137 | ||||||||
\(705\) | −0.160428 | −0.00604207 | ||||||||
\(706\) | −4.16675 | −0.156818 | ||||||||
\(707\) | 18.7334 | 0.704544 | ||||||||
\(708\) | 3.53802 | 0.132967 | ||||||||
\(709\) | −22.7340 | −0.853793 | −0.426896 | − | 0.904301i | \(-0.640393\pi\) | ||||
−0.426896 | + | 0.904301i | \(0.640393\pi\) | |||||||
\(710\) | −0.877634 | −0.0329370 | ||||||||
\(711\) | −39.8893 | −1.49597 | ||||||||
\(712\) | 168.701 | 6.32235 | ||||||||
\(713\) | −7.48726 | −0.280400 | ||||||||
\(714\) | 2.42581 | 0.0907838 | ||||||||
\(715\) | −1.90309 | −0.0711717 | ||||||||
\(716\) | 77.5116 | 2.89674 | ||||||||
\(717\) | 13.2707 | 0.495605 | ||||||||
\(718\) | 59.6590 | 2.22646 | ||||||||
\(719\) | 48.6196 | 1.81320 | 0.906602 | − | 0.421986i | \(-0.138667\pi\) | ||||
0.906602 | + | 0.421986i | \(0.138667\pi\) | |||||||
\(720\) | 34.3230 | 1.27914 | ||||||||
\(721\) | −31.6210 | −1.17763 | ||||||||
\(722\) | 42.5720 | 1.58437 | ||||||||
\(723\) | −9.54221 | −0.354879 | ||||||||
\(724\) | 20.9929 | 0.780196 | ||||||||
\(725\) | −15.1354 | −0.562116 | ||||||||
\(726\) | 1.35977 | 0.0504659 | ||||||||
\(727\) | −18.8705 | −0.699870 | −0.349935 | − | 0.936774i | \(-0.613796\pi\) | ||||
−0.349935 | + | 0.936774i | \(0.613796\pi\) | |||||||
\(728\) | −49.0321 | −1.81725 | ||||||||
\(729\) | −14.9224 | −0.552680 | ||||||||
\(730\) | 24.6059 | 0.910706 | ||||||||
\(731\) | 1.00000 | 0.0369863 | ||||||||
\(732\) | 38.8812 | 1.43709 | ||||||||
\(733\) | 5.70688 | 0.210788 | 0.105394 | − | 0.994431i | \(-0.466390\pi\) | ||||
0.105394 | + | 0.994431i | \(0.466390\pi\) | |||||||
\(734\) | −33.1710 | −1.22436 | ||||||||
\(735\) | −1.33925 | −0.0493991 | ||||||||
\(736\) | −80.3506 | −2.96176 | ||||||||
\(737\) | −13.3080 | −0.490207 | ||||||||
\(738\) | 36.5356 | 1.34490 | ||||||||
\(739\) | −27.8976 | −1.02623 | −0.513116 | − | 0.858320i | \(-0.671509\pi\) | ||||
−0.513116 | + | 0.858320i | \(0.671509\pi\) | |||||||
\(740\) | −46.1777 | −1.69753 | ||||||||
\(741\) | −2.49172 | −0.0915355 | ||||||||
\(742\) | −26.1649 | −0.960544 | ||||||||
\(743\) | −40.3694 | −1.48101 | −0.740506 | − | 0.672050i | \(-0.765414\pi\) | ||||
−0.740506 | + | 0.672050i | \(0.765414\pi\) | |||||||
\(744\) | −12.9711 | −0.475543 | ||||||||
\(745\) | 8.70928 | 0.319083 | ||||||||
\(746\) | −46.5985 | −1.70609 | ||||||||
\(747\) | 7.31627 | 0.267688 | ||||||||
\(748\) | 5.72614 | 0.209368 | ||||||||
\(749\) | −6.79465 | −0.248271 | ||||||||
\(750\) | 9.25009 | 0.337766 | ||||||||
\(751\) | 24.3300 | 0.887814 | 0.443907 | − | 0.896073i | \(-0.353592\pi\) | ||||
0.443907 | + | 0.896073i | \(0.353592\pi\) | |||||||
\(752\) | −7.92760 | −0.289090 | ||||||||
\(753\) | 5.61582 | 0.204652 | ||||||||
\(754\) | 24.8883 | 0.906379 | ||||||||
\(755\) | 10.1488 | 0.369353 | ||||||||
\(756\) | −28.7880 | −1.04701 | ||||||||
\(757\) | −19.5391 | −0.710161 | −0.355080 | − | 0.934836i | \(-0.615547\pi\) | ||||
−0.355080 | + | 0.934836i | \(0.615547\pi\) | |||||||
\(758\) | 44.4752 | 1.61541 | ||||||||
\(759\) | 1.43073 | 0.0519321 | ||||||||
\(760\) | −14.2566 | −0.517140 | ||||||||
\(761\) | 35.3505 | 1.28145 | 0.640727 | − | 0.767769i | \(-0.278633\pi\) | ||||
0.640727 | + | 0.767769i | \(0.278633\pi\) | |||||||
\(762\) | 20.5718 | 0.745239 | ||||||||
\(763\) | −9.49168 | −0.343622 | ||||||||
\(764\) | 94.7938 | 3.42952 | ||||||||
\(765\) | −1.97983 | −0.0715809 | ||||||||
\(766\) | 43.7565 | 1.58099 | ||||||||
\(767\) | 3.35168 | 0.121022 | ||||||||
\(768\) | −42.0753 | −1.51826 | ||||||||
\(769\) | −9.98347 | −0.360013 | −0.180007 | − | 0.983665i | \(-0.557612\pi\) | ||||
−0.180007 | + | 0.983665i | \(0.557612\pi\) | |||||||
\(770\) | 3.55618 | 0.128156 | ||||||||
\(771\) | 5.36527 | 0.193225 | ||||||||
\(772\) | −88.6744 | −3.19146 | ||||||||
\(773\) | 29.4307 | 1.05855 | 0.529274 | − | 0.848451i | \(-0.322464\pi\) | ||||
0.529274 | + | 0.848451i | \(0.322464\pi\) | |||||||
\(774\) | −7.67358 | −0.275821 | ||||||||
\(775\) | 11.4837 | 0.412506 | ||||||||
\(776\) | −186.520 | −6.69566 | ||||||||
\(777\) | 9.81378 | 0.352067 | ||||||||
\(778\) | 83.0925 | 2.97901 | ||||||||
\(779\) | −9.13867 | −0.327427 | ||||||||
\(780\) | −5.33098 | −0.190880 | ||||||||
\(781\) | 0.440272 | 0.0157542 | ||||||||
\(782\) | 8.12929 | 0.290703 | ||||||||
\(783\) | 9.50876 | 0.339816 | ||||||||
\(784\) | −66.1797 | −2.36356 | ||||||||
\(785\) | 5.96754 | 0.212991 | ||||||||
\(786\) | −7.62681 | −0.272039 | ||||||||
\(787\) | −19.1425 | −0.682357 | −0.341179 | − | 0.939998i | \(-0.610826\pi\) | ||||
−0.341179 | + | 0.939998i | \(0.610826\pi\) | |||||||
\(788\) | −8.38785 | −0.298805 | ||||||||
\(789\) | 7.12430 | 0.253632 | ||||||||
\(790\) | 28.8026 | 1.02475 | ||||||||
\(791\) | −17.0230 | −0.605268 | ||||||||
\(792\) | −28.5928 | −1.01600 | ||||||||
\(793\) | 36.8335 | 1.30800 | ||||||||
\(794\) | −42.7957 | −1.51876 | ||||||||
\(795\) | −1.85115 | −0.0656536 | ||||||||
\(796\) | −60.7509 | −2.15326 | ||||||||
\(797\) | 25.0016 | 0.885604 | 0.442802 | − | 0.896620i | \(-0.353985\pi\) | ||||
0.442802 | + | 0.896620i | \(0.353985\pi\) | |||||||
\(798\) | 4.65609 | 0.164824 | ||||||||
\(799\) | 0.457282 | 0.0161775 | ||||||||
\(800\) | 123.239 | 4.35715 | ||||||||
\(801\) | 44.9672 | 1.58884 | ||||||||
\(802\) | −26.0441 | −0.919648 | ||||||||
\(803\) | −12.3438 | −0.435602 | ||||||||
\(804\) | −37.2786 | −1.31472 | ||||||||
\(805\) | 3.74174 | 0.131879 | ||||||||
\(806\) | −18.8835 | −0.665142 | ||||||||
\(807\) | −10.2956 | −0.362422 | ||||||||
\(808\) | 108.759 | 3.82614 | ||||||||
\(809\) | 48.9099 | 1.71958 | 0.859790 | − | 0.510648i | \(-0.170594\pi\) | ||||
0.859790 | + | 0.510648i | \(0.170594\pi\) | |||||||
\(810\) | 13.7612 | 0.483521 | ||||||||
\(811\) | −32.1108 | −1.12756 | −0.563781 | − | 0.825924i | \(-0.690654\pi\) | ||||
−0.563781 | + | 0.825924i | \(0.690654\pi\) | |||||||
\(812\) | −34.4682 | −1.20960 | ||||||||
\(813\) | 8.32891 | 0.292108 | ||||||||
\(814\) | 31.2566 | 1.09554 | ||||||||
\(815\) | −12.5329 | −0.439007 | ||||||||
\(816\) | 8.48091 | 0.296891 | ||||||||
\(817\) | 1.91939 | 0.0671511 | ||||||||
\(818\) | 24.7227 | 0.864409 | ||||||||
\(819\) | −13.0695 | −0.456684 | ||||||||
\(820\) | −19.5520 | −0.682786 | ||||||||
\(821\) | −17.1261 | −0.597704 | −0.298852 | − | 0.954299i | \(-0.596604\pi\) | ||||
−0.298852 | + | 0.954299i | \(0.596604\pi\) | |||||||
\(822\) | −3.28342 | −0.114522 | ||||||||
\(823\) | −16.1851 | −0.564176 | −0.282088 | − | 0.959389i | \(-0.591027\pi\) | ||||
−0.282088 | + | 0.959389i | \(0.591027\pi\) | |||||||
\(824\) | −183.580 | −6.39530 | ||||||||
\(825\) | −2.19439 | −0.0763990 | ||||||||
\(826\) | −6.26305 | −0.217919 | ||||||||
\(827\) | 46.5392 | 1.61833 | 0.809163 | − | 0.587584i | \(-0.199921\pi\) | ||||
0.809163 | + | 0.587584i | \(0.199921\pi\) | |||||||
\(828\) | −46.2328 | −1.60670 | ||||||||
\(829\) | 39.8359 | 1.38356 | 0.691778 | − | 0.722110i | \(-0.256828\pi\) | ||||
0.691778 | + | 0.722110i | \(0.256828\pi\) | |||||||
\(830\) | −5.28281 | −0.183369 | ||||||||
\(831\) | 3.58835 | 0.124479 | ||||||||
\(832\) | −110.640 | −3.83576 | ||||||||
\(833\) | 3.81739 | 0.132265 | ||||||||
\(834\) | 3.59960 | 0.124644 | ||||||||
\(835\) | 15.6102 | 0.540213 | ||||||||
\(836\) | 10.9907 | 0.380122 | ||||||||
\(837\) | −7.21457 | −0.249372 | ||||||||
\(838\) | −8.72136 | −0.301275 | ||||||||
\(839\) | −15.0363 | −0.519110 | −0.259555 | − | 0.965728i | \(-0.583576\pi\) | ||||
−0.259555 | + | 0.965728i | \(0.583576\pi\) | |||||||
\(840\) | 6.48227 | 0.223660 | ||||||||
\(841\) | −17.6151 | −0.607416 | ||||||||
\(842\) | −33.0531 | −1.13909 | ||||||||
\(843\) | 2.66716 | 0.0918620 | ||||||||
\(844\) | −45.8679 | −1.57884 | ||||||||
\(845\) | 4.27276 | 0.146987 | ||||||||
\(846\) | −3.50899 | −0.120642 | ||||||||
\(847\) | −1.78399 | −0.0612985 | ||||||||
\(848\) | −91.4754 | −3.14128 | ||||||||
\(849\) | 4.56807 | 0.156776 | ||||||||
\(850\) | −12.4684 | −0.427663 | ||||||||
\(851\) | 32.8876 | 1.12737 | ||||||||
\(852\) | 1.23330 | 0.0422521 | ||||||||
\(853\) | −1.78880 | −0.0612473 | −0.0306237 | − | 0.999531i | \(-0.509749\pi\) | ||||
−0.0306237 | + | 0.999531i | \(0.509749\pi\) | |||||||
\(854\) | −68.8282 | −2.35525 | ||||||||
\(855\) | −3.80007 | −0.129960 | ||||||||
\(856\) | −39.4472 | −1.34828 | ||||||||
\(857\) | 15.7528 | 0.538105 | 0.269052 | − | 0.963126i | \(-0.413290\pi\) | ||||
0.269052 | + | 0.963126i | \(0.413290\pi\) | |||||||
\(858\) | 3.60841 | 0.123189 | ||||||||
\(859\) | 17.9930 | 0.613912 | 0.306956 | − | 0.951724i | \(-0.400690\pi\) | ||||
0.306956 | + | 0.951724i | \(0.400690\pi\) | |||||||
\(860\) | 4.10651 | 0.140031 | ||||||||
\(861\) | 4.15523 | 0.141610 | ||||||||
\(862\) | −25.1295 | −0.855913 | ||||||||
\(863\) | 9.28236 | 0.315975 | 0.157988 | − | 0.987441i | \(-0.449499\pi\) | ||||
0.157988 | + | 0.987441i | \(0.449499\pi\) | |||||||
\(864\) | −77.4242 | −2.63402 | ||||||||
\(865\) | −17.6341 | −0.599576 | ||||||||
\(866\) | 96.1747 | 3.26815 | ||||||||
\(867\) | −0.489198 | −0.0166140 | ||||||||
\(868\) | 26.1520 | 0.887656 | ||||||||
\(869\) | −14.4491 | −0.490151 | ||||||||
\(870\) | −3.29035 | −0.111553 | ||||||||
\(871\) | −35.3153 | −1.19661 | ||||||||
\(872\) | −55.1050 | −1.86609 | ||||||||
\(873\) | −49.7166 | −1.68265 | ||||||||
\(874\) | 15.6033 | 0.527790 | ||||||||
\(875\) | −12.1359 | −0.410268 | ||||||||
\(876\) | −34.5775 | −1.16827 | ||||||||
\(877\) | −40.7755 | −1.37689 | −0.688446 | − | 0.725287i | \(-0.741707\pi\) | ||||
−0.688446 | + | 0.725287i | \(0.741707\pi\) | |||||||
\(878\) | −67.3943 | −2.27445 | ||||||||
\(879\) | −2.64090 | −0.0890755 | ||||||||
\(880\) | 12.4328 | 0.419109 | ||||||||
\(881\) | 38.0087 | 1.28054 | 0.640272 | − | 0.768148i | \(-0.278822\pi\) | ||||
0.640272 | + | 0.768148i | \(0.278822\pi\) | |||||||
\(882\) | −29.2931 | −0.986349 | ||||||||
\(883\) | 16.1164 | 0.542360 | 0.271180 | − | 0.962529i | \(-0.412586\pi\) | ||||
0.271180 | + | 0.962529i | \(0.412586\pi\) | |||||||
\(884\) | 15.1954 | 0.511075 | ||||||||
\(885\) | −0.443108 | −0.0148949 | ||||||||
\(886\) | 63.8690 | 2.14572 | ||||||||
\(887\) | 1.51048 | 0.0507171 | 0.0253586 | − | 0.999678i | \(-0.491927\pi\) | ||||
0.0253586 | + | 0.999678i | \(0.491927\pi\) | |||||||
\(888\) | 56.9750 | 1.91196 | ||||||||
\(889\) | −26.9897 | −0.905206 | ||||||||
\(890\) | −32.4692 | −1.08837 | ||||||||
\(891\) | −6.90344 | −0.231274 | ||||||||
\(892\) | −65.1117 | −2.18010 | ||||||||
\(893\) | 0.877705 | 0.0293713 | ||||||||
\(894\) | −16.5134 | −0.552292 | ||||||||
\(895\) | −9.70769 | −0.324492 | ||||||||
\(896\) | 108.720 | 3.63209 | ||||||||
\(897\) | 3.79670 | 0.126768 | ||||||||
\(898\) | 52.8122 | 1.76237 | ||||||||
\(899\) | −8.63807 | −0.288096 | ||||||||
\(900\) | 70.9101 | 2.36367 | ||||||||
\(901\) | 5.27651 | 0.175786 | ||||||||
\(902\) | 13.2343 | 0.440653 | ||||||||
\(903\) | −0.872723 | −0.0290424 | ||||||||
\(904\) | −98.8291 | −3.28701 | ||||||||
\(905\) | −2.62919 | −0.0873973 | ||||||||
\(906\) | −19.2429 | −0.639302 | ||||||||
\(907\) | 1.89086 | 0.0627850 | 0.0313925 | − | 0.999507i | \(-0.490006\pi\) | ||||
0.0313925 | + | 0.999507i | \(0.490006\pi\) | |||||||
\(908\) | −84.2819 | −2.79699 | ||||||||
\(909\) | 28.9897 | 0.961526 | ||||||||
\(910\) | 9.43698 | 0.312833 | ||||||||
\(911\) | 45.9887 | 1.52367 | 0.761837 | − | 0.647769i | \(-0.224298\pi\) | ||||
0.761837 | + | 0.647769i | \(0.224298\pi\) | |||||||
\(912\) | 16.2782 | 0.539026 | ||||||||
\(913\) | 2.65016 | 0.0877076 | ||||||||
\(914\) | −16.3031 | −0.539257 | ||||||||
\(915\) | −4.86956 | −0.160983 | ||||||||
\(916\) | 89.4337 | 2.95497 | ||||||||
\(917\) | 10.0062 | 0.330433 | ||||||||
\(918\) | 7.83322 | 0.258535 | ||||||||
\(919\) | 32.8636 | 1.08407 | 0.542035 | − | 0.840356i | \(-0.317654\pi\) | ||||
0.542035 | + | 0.840356i | \(0.317654\pi\) | |||||||
\(920\) | 21.7231 | 0.716190 | ||||||||
\(921\) | −11.3002 | −0.372353 | ||||||||
\(922\) | −64.5918 | −2.12722 | ||||||||
\(923\) | 1.16834 | 0.0384565 | ||||||||
\(924\) | −4.99733 | −0.164400 | ||||||||
\(925\) | −50.4417 | −1.65851 | ||||||||
\(926\) | 88.6699 | 2.91388 | ||||||||
\(927\) | −48.9329 | −1.60717 | ||||||||
\(928\) | −92.7006 | −3.04305 | ||||||||
\(929\) | −12.3825 | −0.406258 | −0.203129 | − | 0.979152i | \(-0.565111\pi\) | ||||
−0.203129 | + | 0.979152i | \(0.565111\pi\) | |||||||
\(930\) | 2.49648 | 0.0818629 | ||||||||
\(931\) | 7.32708 | 0.240136 | ||||||||
\(932\) | −117.421 | −3.84624 | ||||||||
\(933\) | −9.47992 | −0.310359 | ||||||||
\(934\) | −32.8091 | −1.07355 | ||||||||
\(935\) | −0.717152 | −0.0234534 | ||||||||
\(936\) | −75.8763 | −2.48009 | ||||||||
\(937\) | −33.0716 | −1.08040 | −0.540201 | − | 0.841536i | \(-0.681652\pi\) | ||||
−0.540201 | + | 0.841536i | \(0.681652\pi\) | |||||||
\(938\) | 65.9912 | 2.15469 | ||||||||
\(939\) | −12.4381 | −0.405903 | ||||||||
\(940\) | 1.87783 | 0.0612481 | ||||||||
\(941\) | 26.2525 | 0.855807 | 0.427903 | − | 0.903824i | \(-0.359252\pi\) | ||||
0.427903 | + | 0.903824i | \(0.359252\pi\) | |||||||
\(942\) | −11.3149 | −0.368659 | ||||||||
\(943\) | 13.9248 | 0.453455 | ||||||||
\(944\) | −21.8963 | −0.712665 | ||||||||
\(945\) | 3.60547 | 0.117286 | ||||||||
\(946\) | −2.77959 | −0.0903724 | ||||||||
\(947\) | 2.26808 | 0.0737026 | 0.0368513 | − | 0.999321i | \(-0.488267\pi\) | ||||
0.0368513 | + | 0.999321i | \(0.488267\pi\) | |||||||
\(948\) | −40.4749 | −1.31456 | ||||||||
\(949\) | −32.7564 | −1.06332 | ||||||||
\(950\) | −23.9318 | −0.776449 | ||||||||
\(951\) | 13.1402 | 0.426101 | ||||||||
\(952\) | −18.4770 | −0.598843 | ||||||||
\(953\) | −49.8224 | −1.61391 | −0.806953 | − | 0.590615i | \(-0.798885\pi\) | ||||
−0.806953 | + | 0.590615i | \(0.798885\pi\) | |||||||
\(954\) | −40.4897 | −1.31090 | ||||||||
\(955\) | −11.8721 | −0.384174 | ||||||||
\(956\) | −155.336 | −5.02392 | ||||||||
\(957\) | 1.65063 | 0.0533573 | ||||||||
\(958\) | −71.4177 | −2.30740 | ||||||||
\(959\) | 4.30776 | 0.139105 | ||||||||
\(960\) | 14.6272 | 0.472089 | ||||||||
\(961\) | −24.4461 | −0.788582 | ||||||||
\(962\) | 82.9451 | 2.67426 | ||||||||
\(963\) | −10.5146 | −0.338828 | ||||||||
\(964\) | 111.693 | 3.59739 | ||||||||
\(965\) | 11.1057 | 0.357506 | ||||||||
\(966\) | −7.09462 | −0.228266 | ||||||||
\(967\) | −35.5401 | −1.14289 | −0.571446 | − | 0.820639i | \(-0.693617\pi\) | ||||
−0.571446 | + | 0.820639i | \(0.693617\pi\) | |||||||
\(968\) | −10.3571 | −0.332891 | ||||||||
\(969\) | −0.938964 | −0.0301639 | ||||||||
\(970\) | 35.8985 | 1.15263 | ||||||||
\(971\) | 20.1539 | 0.646770 | 0.323385 | − | 0.946267i | \(-0.395179\pi\) | ||||
0.323385 | + | 0.946267i | \(0.395179\pi\) | |||||||
\(972\) | −67.7488 | −2.17304 | ||||||||
\(973\) | −4.72258 | −0.151399 | ||||||||
\(974\) | −52.2288 | −1.67352 | ||||||||
\(975\) | −5.82323 | −0.186493 | ||||||||
\(976\) | −240.631 | −7.70241 | ||||||||
\(977\) | −16.2581 | −0.520143 | −0.260071 | − | 0.965589i | \(-0.583746\pi\) | ||||
−0.260071 | + | 0.965589i | \(0.583746\pi\) | |||||||
\(978\) | 23.7632 | 0.759864 | ||||||||
\(979\) | 16.2884 | 0.520580 | ||||||||
\(980\) | 15.6762 | 0.500756 | ||||||||
\(981\) | −14.6882 | −0.468958 | ||||||||
\(982\) | 2.04326 | 0.0652031 | ||||||||
\(983\) | 8.37311 | 0.267061 | 0.133530 | − | 0.991045i | \(-0.457369\pi\) | ||||
0.133530 | + | 0.991045i | \(0.457369\pi\) | |||||||
\(984\) | 24.1237 | 0.769035 | ||||||||
\(985\) | 1.05051 | 0.0334720 | ||||||||
\(986\) | 9.37878 | 0.298681 | ||||||||
\(987\) | −0.399080 | −0.0127029 | ||||||||
\(988\) | 29.1659 | 0.927890 | ||||||||
\(989\) | −2.92463 | −0.0929980 | ||||||||
\(990\) | 5.50312 | 0.174901 | ||||||||
\(991\) | 46.4511 | 1.47557 | 0.737783 | − | 0.675037i | \(-0.235873\pi\) | ||||
0.737783 | + | 0.675037i | \(0.235873\pi\) | |||||||
\(992\) | 70.3346 | 2.23313 | ||||||||
\(993\) | −2.46650 | −0.0782719 | ||||||||
\(994\) | −2.18320 | −0.0692470 | ||||||||
\(995\) | 7.60855 | 0.241207 | ||||||||
\(996\) | 7.42368 | 0.235228 | ||||||||
\(997\) | −41.5361 | −1.31546 | −0.657730 | − | 0.753254i | \(-0.728483\pi\) | ||||
−0.657730 | + | 0.753254i | \(0.728483\pi\) | |||||||
\(998\) | 49.4691 | 1.56592 | ||||||||
\(999\) | 31.6898 | 1.00262 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8041.2.a.h.1.1 | ✓ | 74 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8041.2.a.h.1.1 | ✓ | 74 | 1.1 | even | 1 | trivial |